The fluorescence decay of the excited state of most biopolymers, and biopolymer conjugates and complexes, is not, in general, a simple exponential. The method of moments is used to establish a means of analyzing such multi-exponential decays. The method is tested by the use of computer simulated data, assuming that the limiting error is determined by noise generated by a pseudorandom number generator. Multi-exponential systems with relatively closely spaced decay constants may be successfully analyzed. The analyses show the requirements, in terms of precision, that data must meet. The results may be used both as an aid in the design of equipment and in the analysis of data subsequently obtained.

The method of moments, as presented by Isenberg and Dyson (1969; Biophys. J. 9:1337) has been shown to be a reliable way of obtaining the amplitudes and time constants of several simultaneously emitting species, even in the presence of an overlapping excitation. Recent improvements in the method include (a) a component incrementation test for determining the number of relaxations, (b) a procedure, which we call exponential depression, for dramatically improving convergence, and (c) a new algorithm for implementing the method of moments on a digital computer with a high degree of flexibility and efficiency. These improvements, as well as new general theory, are described and tested using both synthetic and real experimental data. Component incrementation consists of examining models with increasing numbers of exponential terms. Given adequate precision, we find that an analysis for N + 1 components, of data that are actually represented by N components, provides the correct amplitudes and time constants plus an N + 1 term with an insignificant amplitude. Exponential depression is a transformation in which the original excitation and fluorescence, E(t) and F(t), are multiplied by exp (-lambdat), where lambda is an arbitrary parameter. While the convolution is invariant to this transformation, the proper choice of lambda greatly reduces the number of iterations necessary to obtain the amplitudes and time constants and may even improve their accuracy. In addition, an appendix by John P. Mullooly presents a statistical analysis of the effect of counting error on the method of moments estimates of fluorescence decay parameters, applicable when data are obtained by the monophoton technique. Formulas are derived that give the approximate precision of the decay parameters for the general case of N exponential components, with calculational details for one and two component systems.

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The purpose of this study was to examine the pyruvate kinase isozymic patterns of a wide variety of tissues from rats and mice, particularly regarding hybrid isozymes. For these studies, we employed longer electrophoresis times than used in most earlier studies in order to improve the resolution of closely spaced bands. The tissue distributions of types K, L, and M pyruvate kinases were found to be approximately the same as those reported earlier for rats and other mammals. In addition, K-M hybrids could be detected in most tissues examined in relative quantities which differed from one tissue to another in the same organism, in corresponding tissues from different species, and within a single tissue during development. Hybrid isozymes containing type L subunits occur in only a few tissues of either the fetus or the adult of either animal. In earlier studies utilizing L-M hybrid isozymes produced in vitro, we showed that the kinetic properties of a given subunit are profoundly affected by the nature of its neighbors within the tetramer (Dyson and Cardenas, ['73] J. Biol. Chem., 248: 8482-8488). Based on these altered kinetic properties, we suggest that there is little need for anorganism to suppress completely the gene activity for one subunit type of pyruvate kinase during the synthesis of larger quantities of a second subunit type.